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Article

Reviel Netz

Like all other people the Greeks counted, measured and taught such skills to their young. Such practices in the classical Mediterranean were mostly continuous with those of the ancient Near East. The Babylonian base 60 found its way into Greek coin values, the Near Eastern Abacus— probably a Semitic word—was widely used, and mathematical education in Hellenistic Egypt (as seen in papyri) was closely related to that of Ancient Mesopotamia. At the same time, μαθηματική, at the latest from *Plato(1)'s time onwards, came to refer to something different. Midway between the modern terms ‘mathematics’ and ‘exact sciences’, this was primarily a new genre. It was never pursued by more than a handful of experts (even educated Greeks would know very little about the contents of this genre, though many could know about its existence). This genre formed a radical departure, both externally (from the Ancient Near East) and internally (from other Greek genres). It survived throughout antiquity and essentially remained unchanged in Arabic and Latin forms in the Middle Ages, forming the basis for modern science. Its major achievement was the deductive method: reading a Greek mathematical proof, one finds its validity irresistibly compelling. It may be for this reason that Greek culture, with its emphasis on persuasion, was the one to invent the mathematical genre (Lloyd 1990).

Article

Sylvia Berryman

The ancient Greek mechanical art addressed itself to the manufacture of assorted working artifacts, which were loosely organized into categories that reflected different understandings of the techniques by which they worked. Theories positing mathematical relationships were one reason for regarding groups of devices as part of a technical field; common physical principles governing their operation were another reason. The view that ancient Greek mechanics was regarded as working by magic has been discredited: although mechanics as a field produced “wonders” or show-pieces, this does not seem to have informed the understanding of the technê—a term often translated as art, but bearing implications of systematicity and method—by its practitioners. Aristotle classified mechanics, along with harmonics, astronomy, and optics, as one of the fields intermediate between mathematics and physics (Posterior Analytics 1.13, 78b37; 1.9, 76a24), based on mathematical principles.Balance and weight-lifting technologies, like levers and pulleys, were understood to exhibit mathematical proportions. A weight twice as far from the fulcrum could counterbalance another object twice its weight, or a lever twice as long could be used to raise twice the weight with the same power.

Article

William David Ross and V. Nutton

Medicina Plinii, an extant compilation made (probably 300–50 ce) from *Pliny(1)'s account, in books 20–32 of the Naturalis historia, of the plants and animals used for medicinal purposes. Marcellus Empiricus describes it as being the work of a second Pliny. This work has to be distinguished from a work commonly but falsely ascribed to Plinius Valerianus, of which the first three books are a garbled version (6th or 7th cent.) of the earlier work, while the last two books come from a different source.

Article

J. T. Vallance

Western literature begins with a *disease; in the first book of Homer'sIliad the god *Apollo (associated with the medical arts directly or through his Asclepiad progeny; see Asclepius) sends a plague on the Greeks camped before Troy to avenge Chryses' treatment at the hands of *Agamemnon. No attempt is made to treat the plague; the activity of doctors in the Homeric epics is generally limited to the treatment of wounds and injuries sustained in combat. Many later authorities (e.g. A. *Cornelius Celsus) argued that this was a sign of the high moral standards which then prevailed. If disease had its own moral force in literature—note, for example, Hesiod's account of diseases escaping from *Pandora's jar (Op.69–105), the role of illness and *deformity in the *Oedipus legends, in *Sophocles' Philoctetes, in Attic comedy, and down to the Roman Stoic (see Stoicism) disapproval of over-reliance on medical help—the status and social function of those who treated diseases was similarly a matter for moral ambivalence.

Article

John Z. Wee

Cuneiform medical manuscripts are found in large numbers, mostly from 1st-millennium bce sites throughout ancient Mesopotamia. Included in the therapeutic tradition are pharmacological glossaries, herbal recipes with plant, mineral, and animal ingredients, and healing incantations and rituals. A Diagnostic Handbook created at the end of the 2nd millennium bce maps out a blueprint for medical practice that sketches out how a healer progresses in his knowledge of the sickness—initially interpreting bodily signs in ways reminiscent of omen divination, and only later arriving at a settled diagnostic verdict and treatment of the kind depicted in the therapeutic tradition. Mesopotamian aetiologies focused on malevolent agents external to the body, encouraging concerns for contagion, prophylaxis, and sanitation, while omitting significant roles for dietetics and exercise aimed at rectifying internal imbalances. Operative surgery was limited, because of the inadequacy of available analgesics and antiseptics. Suppliants seeking a cure visited temples of the healing goddess Gula in the cities of Isin and Nippur, while, among the professions, the “magician” and the “physician” were most associated with medical practice. After the 5th century bce, Calendar Texts and other astrological genres linked various ingredients to each zodiacal name, indicating certain days when a particular ingredient would become medically efficacious.

Article

Melampus (2) (3rd cent. bce), author of two extant works on *divination, Περὶ παλμῶν μαντικῆς (‘On Divination by Palpitation’: ed. H. Diels, Abh. Berl. Akad.1907) and Περὶ ἐλαιῶν τοῦ σώματος (‘On Birthmarks’: ed. J. G. F. Franz, Scriptores Physiognomoniae Veteres, 1780).

Article

Menaechmus (2) (fl. mid-4th cent. bce), geometer, disciple of *Eudoxus(1) of Cnidus, offered a solution of the problem of two mean proportionals. A text of the solution is reported in the Archimedes commentary by Eutocius of Ascalon. As the solution employs conic sections (a hyperbola and two parabolas), Menaechmus must have anticipated in some manner the theory of conic sections, first compiled about a half-century later by *Euclid and by the mathematician Aristaeus of Croton.

Article

Menelaus (3), of *Alexandria (1 (fl. 95–8 ce), mathematician and astronomer, made astronomical observations at Rome in 98 (Ptol. Alm. 7. 3), and was known to *Plutarch (De fac. 17). The following works by him are extant (only in Arabic translation). (1) Sphaerica, in three books, is a textbook of spherical geometry, which contains the earliest theorems on spherical trigonometry. Book 1 gives the definition of a spherical triangle (τρίπλευρον), and develops theorems modelled on Euclid's for the plane triangle. Book 2 is concerned with the solution of problems important for spherical astronomy, in a more elegant way than such predecessors as *Theodosius(4). Book 3 treats the basis of spherical trigonometry. Proposition 1 is ‘Menelaus' Theorem’, which was used by subsequent astronomers (e.g. *Ptolemy(4)) to solve spherical triangles. It is probable that much of this treatise was original: it superseded earlier methods of solving spherical problems (see trigonometry).

Article

A south-Italian Greekbotanist, traditionally a Pythagorean (see Pythagoras(1)) from *Sybaris (Iamb.VP 267). *Theophrastus occasionally quotes from Menestor's lost books on botany, which considered particular plants and their growth according to warmth or frigidity. Mulberries sprout late, but ripen quickly, growing in cold weather (Theophr.Caus. pl. 1. 17. 3), an application of the Pythagorean theory of opposition of the warmth and cold to plants: mulberry requires cold for growth, from its warm nature. Plants needing warmth due to their cold nature included rush, reed, galingale, silver fir, pine, prickly cedar, Phoenician cedar, and ivy (ibid. 1. 21. 6). *Empedocles had posited a theory of why the warm evergreens withstood cold weather by means of their pores, so Menestor is dated sometime between Empedocles and Theophrastus (c.400 bce), and is the author of the first known Greek works on inductive botany. Theophrastus (Causis pl.

Article

Meno  

J. T. Vallance

Pupil of *Aristotle. His summary of medical doctrines was known to *Plutarch (Quaest. conv. 8. 9. 3) and *Galen (15. 25 Kühn). Parts are thought to be preserved in the ‘Anonymus Londinensis’ papyrus, which is one of the most important sources for the early history of Greek *medicine.

Article

Menodotus (3) of *Nicomedi (fl. probably c. 120ce), follower of *Pyrrhon, pupil of *Antiochus (11) of Ascalon, and leader of the empirical school of medicine (see medicine, § 5. 3). He was a voluminous author, and is often referred to by *Galen.

Article

Sandra Blakely

The story of metallurgy in ancient Greece spans five millennia and a geographic range reaching from the Greek colonies in the west to Anatolia and the Levant. An interdisciplinary effort, its study engages archaeological fieldwork, historical texts, and scientific analyses, and has moved from social evolutionary models through Marxist, processual, and post-processual frameworks. Metallurgical innovation and invention are productive loci for the investigation of historical change and emerging complexity. Three case studies—the transition from native ores to smelting, the emergence of bronze, and the spread of iron technology—foreground the entanglement of metallurgy with ecological strategies, maritime and overland mobility, the status of the crafter, and elite and non-elite control of production. Deterministic paradigms and models based on revolutionary innovations are yielding to more nuanced frameworks of gradual change, tempered by insights from ethnoarchaeology and from new excavations which shed fresh light on the cultural meanings of metallurgy among both metalworkers and patrons.

Article

Jonathan Edmondson

In the Roman period most metals were obtained not in a natural state directly from mining, but as a result of metallurgical processing of compound mineral deposits (ores). Ores, once mined, were crushed with stone mortars and as much sterile rock as possible was removed by hand-sorting. Manual millstones, or occasionally handle-powered, ‘hourglass’ mills (similar to the grain-mills from *Pompeii) were used to grind the ore to a powder, which was often further concentrated by washing. This was carried out using portable sievelike instruments or in a permanent installation (washery), where water was channelled over the ore, forcing the heavier metal-bearing grains to settle in basins while carrying off the lighter dross.Few complete Roman smelting-furnaces have survived, and so knowledge of metallurgical techniques depends on scattered finds of parts of furnaces and on ancient authors such as *Diodorus (3) Siculus, *Strabo, and the elder *Pliny(1), who describe the main techniques, sometimes conflating different processes.

Article

J. T. Vallance

Strictly means ‘the study of things aloft’, but the term was widely used in antiquity to cover the study both of what might now be called meteorological phenomena and the investigation of (supposedly) related phenomena on and within the earth itself, such as tides, earthquakes, volcanoes, and the formation of minerals and metals. Presocratic interest in meteorology is well attested, but the difficulty of providing explanations of such intractable phenomena sometimes made students of the subject figures of fun. *Aristophanes (1) in the Clouds parodies ‘meteorosophists’ for their arcane and silly speculations about atmospheric and subterranean marvels. The author of the Hippocratic treatise On Ancient Medicine (see Hippocrates(2)) attacks those who are forced by the very nature of the subject to base their speculations on indemonstrable premisses (see hypothesis, scientific). Even *Socrates (in Plato's Phaedrus 270a) offers *Anaxagoras a backhanded compliment, claiming that he filled people with ‘lofty’ (i.e. meteorological) thoughts.

Article

Marquis Berrey

Methodists were a self-identified medical sect of the 1st century bce, Imperial period, and late antiquity who shared a common method of observation and causal inference about the practice of medicine. Methodists took their name from the “method” (Gk. methodos), an observable path or evidence-based medicine which the physician undertook to gain secure therapeutic knowledge. The path was supposed to reveal the general similarity between patients’ ostensibly differing conditions. Three similarities, or “commonalities,” as they were called, were possible: fluid, constricted, or a mixture of the two. Opponents pilloried Methodists for the loose logic of their methodological revolution and socially disruptive claims to teach medicine within six months. Primarily a Roman phenomenon, the popularity of Methodism seems to have been due to a ready supply of practitioners and its focus on certain, fast therapy. Methodists wrote chiefly on internal medicine, surgery, and medical history.Methodists (Gk. methodikoi, Lat. methodici.

Article

G. J. Toomer and Alexander Jones

Meton, Athenian astronomer, is dated by his observation of the summer solstice, together with *Euctemon, in 432 bce (Ptol. Alm. 3. 1). He is famous for his introduction of the luni-solar calendaric cycle named after him, with 19 solar years and 235 months, of which 110 were ‘hollow’ (containing 29 days) and 125 full (containing 30 days), making a total of 6,940 days. The basis of the cycle (though not the year-length of 365 5/19 days) was undoubtedly derived from Babylonian practice. We may presume that Meton intercalated a thirteenth month in the same years as the Babylonians, and prescribed a fixed sequence of full and hollow months, but this is conjectural. He used the month-names of the Athenian calendar, but his cycle was intended not as a reform of that, but to provide a fixed basis for dating astronomical observations (in which it was later superseded by the cycle of *Callippus), and for Meton's own astronomical calendar (parapēgma).

Article

Grégory Chambon

The study of metrology in the Ancient Near East has, since the 19th century, approached ancient political and economical reality by quantifying and estimating, among other things, the dimensions of urban centres and the number of rations, or war booty, delivered to palaces. A new interdisciplinary practice, from the perspective of the social and cultural history of Mesopotamian metrology, has developed over the last few decades, taking into account the scribal background and weighing and measuring practices in daily life.

The study of metrology has always been important for archaeologists and philologists of the Ancient Near East. Since the first decipherments of cuneiform writing and the first excavations in the 19th centuryce, metrological research has usually focused on reconstructing the relative values in each measures system (capacity, length, area, weight), that is to say, the values by which one unit of the system was converted into another, either as a multiple or a submultiple, as well as of identifying the absolute values of these units, expressed in our modern system (litre, kilogram, meter, etc.). Metrology has been traditionally used for economic history of the Ancient Near East, by providing quantitative data which inform us about, among other things, livestock farming, available resources in the organizing communities (households, cities, temples, and palaces), commercial transactions, or war booty. This led to the Marvin Powell’s synthesis in the 1980s, which still represents a key reference work in ancient Near Eastern research.

Article

Andrew M. Riggsby

There is a large body of evidence for Roman use of weights and measures. In theory, they would have been able to measure a variety of quantities with great precision, given the variety of different-sized units at their disposal and an elaborate system of fractional subdivisions of those units. Moreover, those measurements could have been accurate with respect to a shared system because of publicly available exemplary standards, a theoretical connection between the definitions of the most important measurements, and the existence of state officials who could enforce the standards. As a result, Romans could, in principle, have conveyed very specific metrological information across a great deal of space and time. In practice, measurement was considerably less predictable and less precise. Actual measurement did not necessarily avail itself of the full resources of the theoretical system, and sometimes did not appeal to any general system. Moreover, overtly competing systems coexisted with the “official” ones at all times. Finally, it is not clear how coherent that official system was, nor were the actual systems of enforcement particularly robust. As a result, measurement was often imprecise and/or tightly localized (which probably generated weak expectations of being able to replicate measurement across different contexts).

Article

milk  

Robert Sallares

Fresh milk (γάλα, lac) was not very important in the Greek and Roman diet, for climatic reasons, and many people in southern Italy and Greece cannot digest lactose in milk. However, northern *barbarians, especially nomads like the *Scythians, were known to drink milk. The milk that was consumed, normally in the form of cheese or curds (ὀξύγαλα), was usually that of goats or sheep. Cows' milk found little favour. Butter (βούτυρον) was used only by barbarians, since the Greeks and Romans preferred *olive oil. Horses' milk was also known. Receptacles identified as feeding-bottles for infants have been found on archaeological sites, but breast-milk was much more important (see breast-feeding). Milk was highly valued in medicine. The physicians recommended the internal or external use of milk (both human and animal) or whey for numerous ailments. It was also used for *cosmetic purposes, and in religious ceremonies as a first-fruit offering (see aparchē), although its early use in this domain was often superseded by that of *wine.

Article

mills  

Kevin Greene

Mills ‘Saddle-querns’, in which grain (see cereals) was rubbed between a fixed flat lower stone and a smaller hand-held upper stone, had been in general use for thousands of years before the ‘hopper-rubber’ mill appeared in Greece by the 5th cent. bce. Mechanized versions consisted of a rectangular upper stone, with a cavity that acted as a hopper for grain, pivoted at one end to allow a side-to-side action; grooves cut into the grinding surfaces improved the flow of grain and the removal of flour from the lower stone. Perhaps as early as the 3rd cent. bce, the introduction of a pair of round stones made a dramatic improvement, for a central (adjustable) pivot took the weight of the upper stone, which could be moved in a continuous rotary motion, assisted by its own momentum, and propelled by a crank-like vertical handle set into the upper surface. This development did not take place in Greece, for rotary mills did not appear there before the Roman period. Rotary mills were also scaled up into the hourglass-shaped ‘Pompeian’ form, powered by animals or slaves, in contexts such as commercial bakeries.